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The present work investigated the composition evolution of the TMS series of Ni-base single crystal (SC) superalloys in light of the cluster formula approach systematically. The cluster formula of SC superalloys could be expressed with    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${[}\overline{{{\text{Al}}}} {-} \overline{{{\text{Ni}}}} 12{](}\overline{{{\text{Al}}}} {, }\overline{{{\text{Cr}}}} {)}m$$\end{document}    [   Al  ¯   -   Ni  ¯   12   ]  (    Al  ¯   ,   Cr  ¯   )  m, in which all the alloying elements were classified into three groups, Al series (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\overline{{{\text{Al}}}}$$\end{document}    Al  ¯), Cr series (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\overline{{{\text{Cr}}}}$$\end{document}    Cr  ¯), and Ni series (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\overline{{{\text{Ni}}}}$$\end{document}    Ni  ¯). It was found that the total atom number ( Z ) of the cluster formula units for TMS series of superalloys varies from  Z  ~ 17 to  Z  ~ 15.5, and then to  Z  ~ 16 with the alloy development from the 1st to the 6th generation, in which the superalloys with prominent creep resistance possess an ideal cluster formula of    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$${[}\overline{{{\text{Al}}}} {-} \overline{{{\text{Ni}}}} 12{](}\overline{{{\text{Al}}}} 1.5\overline{{{\text{Cr}}}} 1.5{)}$$\end{document}    [   Al  ¯   -   Ni  ¯   12   ]  (    Al  ¯   1.5   Cr  ¯   1.5  )with  Z  = 16. Similar tendency of composition evolution also appears in the PWA and CMSX series of SC superalloys. Typical TMS series of superalloys with prominent creep properties generally exhibit a moderate lattice misfit of γ/γ′ which could render alloys with appropriate particle size of cuboidal γ′ precipitates to acquire a maximum strength increment by precipitation strengthening mechanism. More importantly, the relationship between the lattice misfit ( δ ) of γ/γ′ and the creep rupture lifetime ( t   r  ) of superalloys was then established, showing a linear correlation in the form of lg t   r  –lg| δ | 3/2  at both conditions of 900 °C/392 MPa and 1100 °C/137 MPa. Combined with the lattice misfit, the cluster formula approach would provide a new way to modify or optimize the compositions of Ni-base superalloys for further improvement of creep property.

Composition rules of Ni-base single crystal superalloys and its influence on creep properties via a cluster formula approach